解题方法
1 . 中国文化中的太极八卦图蕴含了现代哲学中的矛盾对立统一规律,如图1是八卦模型图,其平面图形记为图2中的正八边形
,其中
,若点P是其内部任意一点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b8d017e422f158fe09ed9c867ecfe7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知函数
,将
图像上所有点的横坐标伸长到原来的2倍,而纵坐标保持不变,得到函数
的部分图像如图所示,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b2e285758984e8613fa1b52d674c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6460400186f2b74ece79c861ceb063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
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3 . 已知
,
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266ad08c70080e52495117cb8307fd3d.png)
(1)求函数
的值域;
(2)求函数
,
的单调减区间;
(3)若
,
恰有2个零点
,求实数
的取值范围和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35005965ce7f4b9703cba4062b6f3053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3328a5bbf1db60229da59fbee7675e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266ad08c70080e52495117cb8307fd3d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b0339e96e32d6fa1a092824850ef8d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43281072ba152ac733bbd50550ffe1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86251951bb66bd5b40c2fac797f5c074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
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解题方法
4 . 已知等差数列
,
,……,则该数列的前n项和
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb27896219fcacbcf9e01b99f92a893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa792c87a2ea4947e0a29b30a648cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.无最大值,有最小值 | B.有最大值,无最小值 |
C.有最大值,有最小值 | D.无最大值,无最小值 |
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5 . 若复数
,
满足
.且
(i为虚数单位),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41813be61104fce7a33368d0a4429651.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db439eae71afd7b462a07c61d3861330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b004c02ad0d4d487eb7623f92d306660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41813be61104fce7a33368d0a4429651.png)
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6 . 已知关于
的方程
有四个互不相等的根,若这四个根在复平面上对应的点共圆,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d26154aeb0a3a04910123aec2919a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 对于函数
,给出下列结论:
①函数
的图象关于点
对称;
②函数
的对称轴是
,
;
③若函数
是偶函数,则
的最小值为
;
④函数
在
的值域为
,
其中正确的命题个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c8d435a354619cec663604f939e8bf.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bf205e9f4484245474d6889b168d45.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4293b70e323dcd5d9441767fd6ece384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
③若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a46a0fc7c90b66b3aeb64aa64448eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d061d17bbc13e2d61a0c4aee0cb9ced3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e24f048f9a87274863ba2c037d7a5c.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f1b68c4e44b4fac6780cc7a04b2562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60cbaaa322c6e2ea61db5be77e412a7.png)
其中正确的命题个数是( )
A.0 | B.1 | C.2 | D.3 |
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解题方法
8 . 已知
,
,
.
(1)求
;
(2)若
,求实数k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e310702748855c3edccd151aae0143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b532ff725ed321148010644e7f0e05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7901fc86cb98cdb030d6ee72816dc14a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b195aa36a3c2753ebf08cb464c52ad1e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28366bd942f564a8bc3396dc85b1b73c.png)
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9 . 已知扇形的半径长为5cm,圆心角是2rad,则扇形的弧长是______ cm.
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解题方法
10 . 如图,某快递小哥从A地出发,沿小路
以平均时速20km/h,送快件到C处,已知
,
,
,
,
.
的面积.
(2)快递小哥出发25分钟后,公司发现快件有重大问题,由于通讯不畅,公司只能派车沿大路
追赶,若汽车平均时速50km/h,问汽车能否先到达C处?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722b4403b1cd40188f0bfd1098ec9095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f278de55bd20ebbebf93b2bffa77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9228b213dc6b256b752b38a466ebec93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cab0fa0448c0c400f49ba9a7df49e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3615765e368af8285aef00436f5325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddf607cb6108bd3f726901a5976e2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
(2)快递小哥出发25分钟后,公司发现快件有重大问题,由于通讯不畅,公司只能派车沿大路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574cb9cf21957ecd10ca9bc36a1b0451.png)
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